SOM Question 2023.pdf

318/3(N) March 2023 STRENGTH OF MATERIALS 2886 Ti...

318/3(N) March 2023 STRENGTH OF MATERIALS 2886 Time Allowed: 2.5 Hours Full Marks: 60 Answer toQuestion No. I of Group Ais compulsory and to be answered first. This answer is to be made in separate loose seript(s) provided for the purpose. Maximum time allowed is 30 minutes, after which the loose answer seripts will be colleceted and fresh answer scripts for answering the remaining part of the question will be provided. On early submision of answer seripts of Question No. 1, a student will get the remaining seript earlier. Answer any Five (05) Questions from Group B. Group A 1. Choose the correct answer from the given alternatives (any twenty): lx20 i) The material which shows little or no plastic deformation is called - (a) ductile material (b) brittle material (c) malleable material (d) plastic material. ii) The point at which there is increase in strain with no appreciable increase in stress is known as- (a) Breaking point (b) Yield point (c) Elastic limit (d) Proportional limit. iii) Ratio of Hoop stress and longitudinal stress of a material is equal to - (a) 1(b) ½ (c) 2 (d) none of these. iv) Temperature stress developed in a bar depends upon -(a) co-efficient of linear expansion (b) change of temperature (c) Young's modulus (d) all of these. The area moment of inertia is often called moment of area. (a) first (b) second (c) third (d) fourth vi) Moment of Inertia of a triangular lamina of height 'h' about its base 'b' is - (a) bxhs bxh³ hxb3 12-(b) 36 (c)() none of these. 12 vii) If Iox and Ioy be moments of inertia of a lamina about mutually perpendicular axes OX and OY in the plane of the lamina and Ioz be the moment of inertia of the lamina about an axis 0Z normal to the lamina and passing through the point of intersection of the axis OX and OY then Ioz = lox t loy. The above theorem is known as - (a) theorem of parallel axes (b) theorerm of perpendicular axes (c) three moments theorem (d) none of these. viii) Asimple supported beam of length 10 mcarries uniformly distributed load of 10 KN/m over the entire span. The magnitude of each support reaction will be - (a) 25 kN (b) 30 KN (C) S0 kN (d) 100 kN. ix) The maximum bending moment of a cantilever beam appears at -(a) fixed end (b) free end (c) mid-span (d) none of these. X) If a beam is loaded with UDL, the nature of bending moment diagram will be - (a) straight horizontal line (b) straight inclined line (c) parabolic (d) cubic. xi) At the point of contra flexure, the value of bending moment will be - (a) maximum (b) minimum (c) zero (d) none of these. xii) The bending stress at neutral axis is - (a) maximum (b) minimum (c) zero () tensile in nature. xii) The section modulus of a circular section of diameter d is - (a) nd/32 (b) nd'/32 (c) nd/64 (d) nd'/64. xiv) Neutral axis passes through - (a) the top layer of the beam (b) the bottom layer of the beam (c) the CG of the beam (d) none of these. 1  XV) Maximum deflection of abeam occurs where the slopc of the beam is - (a) maximum (b) 45 (c) 90 (d) o°. xvi) The maximum deflection of a cantilever beam appears at - (a) fixed end (b) free end (c) mid span (d) none of these. Xvìi) Doubling the span of beam will result in incrcase in deflection of the beam by - (a) two times (b) four times (c) eight times (d) none of these. xvi) Euler's fomula for crippling load is best suitable for slenderness ratio more than - (a) 50 (b) 70 (c) 80 (d) 100 xix) The crippling load of a column depends on- (a) cross-sectional area (b) (c) slendermess ratio (d) all of these. modulus of rigidity xx) The ratio of actual length to the equivalent length of a column having one end fixed and other end free is -(a) 1:1 (0) N2:1 (c) 1:2 (4) 1:N2. Xxi) The strength of a hollow shaft for the same length, shaft. -(a) less than (b) more than (c) equal to (d) material and weight is a solid xxii) In pure torsion, the shaft gets deformed due to - (a)none of these. (c) twisting moment only (d) all of these. bending moment only (b) axial load only Xxiii)For a hollow circular shaft torsional shear stress at the centre is - (a) maximum (b) zero (c) minimum (d) none of these. xxiv) The predominant effect of an axial tensile (b) compression (c) twisting (d) tension. force on a helical spring is - (a) bending XXv) Two helical springs of stiffness K is system will be -(a) 2K (b) K/2 (c) 2K attached (d) 4K in parallel. The stiffness of the equivalent Group B 2. i) Draw the stress-strain diagram of Mild ii) A steel wire 2 m long and 3 mm in Steel and locate all the salient points in the diagram. diameter is extended by 0.75 mmn when a weight W is suspended from the wire. If the same weight is suspended from a brass wire, 2.5 m long and 2 mm in diameter, it is elongated by 4.64 mm. that of steel be 2.0 x 10° N/mm Determine the modulus of elasticity of brass if 3+5 3. i) Define volumetric strain and bulk modulus of a i) A copper bar of diameter 25 mm and material, length 2 m is rigidly fixed at both ends. stress induced in the bar if the temperature is Find the 10PC. reduced by 40°C. Take E = 100 GPa, athermal = 16 x 2+6 4. i)State the "Theorem of parallel axis". i) Show that the moment of inertia of a centre of gravity is D°/64, where Dcircular section with respect to an axis passing through its is the diameter of the circular section. 2+6 5. i) Write down the relationship between shear force and bending moment and explain its significance. ii) A simply supported beam 2.5 m long is carrying two point loads of 2 kN and 4 kN at a distance of 1m & 1.5 m from left end respectively. Draw the SF & BM diagram. 2+6 6. i)What are the assumptions in Simple Bending ii) A simply supported beam of span 5 m has Theory? a cross section permissible stress is 10 N/mm, find the maximum intensity of 150 mm x 250 mm. If the uniformly can carry. distributed load it 2+6 7. i) Write the formula for maximum slope of a cantilever beam with a point load at free end. ii) A cantilever beam of 2 m length having width 100 mm and depth 120 mm is subjected to a point load of 30 kN at its free end. Find the maximum slope and deflection at free Young's Modulus of the beam material is 200 GPa. end if the 1+7 2 8 i) What is slenderness ratio? i) Find the Euler's crippling load for a hollow cylindrical steel column of 38 mm external diameter and 2.5 mm thick. Take length of the column as 2.3 mand hinged at its both ends. Take E = 205 GPa. 2+6 9. ) Write down the equation of Pure torsion and explain cach term. i) A solid circular shaft transmits 100 kW power at 200 r.p.m. Calculate the shaft diameter if twist in the shaft is not to exceed 1° in 2metres of the shaft length and the shearing stress is limited to 70 N/mm. Take modulus of rigidity =8x 104 N/mm'. 2+6 10. ) What is Spring index? i) Aclose coil helical spring to carry a load of 250 N, if the mean coil diameter is to be 8 times that of the wire, calculate these diameters. Take maximum shear stress as 70MPa. 2+6 3